Foundations of commercial and industrial buildings, foundations of retaining walls, pile foundations, grade beams and many other structures and structural elements are analyzed and designed as Beams on Elastic Foundation. Methods of analysis of Beams on Elastic Foundation are not limited to the area of Civil-Structural Engineering. These methods are used in various areas of Mechanical and Geotechnical Engineering as well. Analysis of beams on elastic foundation is performed currently by using special computer programs based on numerical methods, such as Finite Difference Method and Finite Element Method. However, these programs are not always available, and their application is limited. Most of computer programs are developed only for Winkler's soil model. They cannot be used for other soil models such as Elastic Half-Space or Elastic Layer and others. Methods of analysis of complex beams, such as stepped beams, pin-connected beams, beams with various boundary conditions are not developed for practical applications. Hand calculations based on Method of End Conditions (Method Hetenyi) or Method of Initial Parameters are very laborious, time consuming and usually impossible to use. Consequently, a practicing engineer has no other option, but to perform hand calculations of any beam on Elastic Foundation as absolutely rigid, without taking into account the actual rigidity of the beam. While this method, in some cases, can be justified, it can also lead to serious mistakes. This book contains tables that allow analyzing various free supported beams on Winkler Foundation. The same tables are used for analysis of complex problems, such as stepped beams, pin-connected beams, interconnected beams, and any other continuous beams with various boundary conditions. This book includes also practical recommendations for analysis of beams and frames on Winkler Foundation by replacing the soil with elastic supports and individual foundations with line elements that allows using programs for analysis of statically indeterminate systems to analyze various beams and frames supported on Elastic Foundation. A significant part of this book is devoted to the Method of Initial Parameters and its application to analysis of Beams and Frames on Elastic Foundation . A computer program, based on this method, allows performing computer analysis of Beams on Elastic Foundation. Stiffness Method is used for combined analysis of frames with continuous foundations. Author takes into account the absolutely rigid elements at the area of intersection of the first floor columns and continuous foundations that significantly specifies the results of analysis. Stiffness Method is also applied to analysis of a system of interconnected beams supported on Winkler Foundation. Proposed method of analysis takes into account the absolutely rigid elements located at the area of beam intersection. The same method is used for analysis of a system of individual foundations connected with grade beams. Numerical examples illustrate application of the described method to practical analysis. A large part of this book is devoted to analysis of Beams and Frames on Elastic Half-Space. A numerical Method proposed by Zshemochkin is further developed and applied to analysis of beams with various boundary conditions and various soil models. Several numerical examples illustrate application of themethod to practical analysis. This book includes also tables developed by Simvulidi that allow analyzing beams supported on Elastic Half-Space. Tables are developed for three types of loads: concentrated vertical loads, moments, and uniformly distributed loads. Application of the tables is also illustrated with a series of numerical examples. Methods of combined analysis of 2D and 3D frames and foundations, described in this book, are relatively simple and produce more accurate results compared to separate analyses of frames and foundations. They allow performing analysis of the system Frame-Foundation using computer programs developed for analysis of regular statically indeterminate systems. While the book does not cover directly analysis of mat foundations, the tables, presented in this book, can, nonetheless, be used for simplified analysis of mats by cutting off bands from the mat in both directions and analyzing each band as a beam supported on Winkler Foundation or on Elastic Half-Space. The primary purpose of this book is to serve the practicing civil and structural engineer, but some parts of the book can also be of outmost interest to graduate students and teachers conducting research in area of structures supported on Elastic Foundation.